User:Rpongcojr

Ito's Lemma


 * $$ dG = \left(\frac{\partial G}{\partial x}a + \frac{\partial G}{\partial t} + \frac{1}{2} \frac{\partial^2 G}{\partial x^2}b^2\right)dt + \frac{\partial G}{\partial x}\,b dz $$

B-S PDE


 * $$ \frac{\partial f}{\partial t} + \frac{1}{2}\sigma^2 S^2\frac{\partial^2 f}{\partial S^2} + r S \frac{\partial f}{\partial S} = r f $$